A thread with some possibly useful info is over at renderosity - you need to be a member - but it’s free.
http://market.renderosity.com/mod/forumpro/showthread.php?thread_id=2648921
It’s difficult to make accurate comments without knowing more about the specifics of what you’re trying to achieve, as there may be totally different approaches available to achieve your desired result. However, a few comments -
Face | PutOn aligns the normals (enable View | Show Normals to see these) of the relevant elements.
Whilst a face must be chosen for the object(s) being moved - this doesn’t apply to the destination element, so you could choose a vert and get more precise / consistent alignment options.
So, if, for example you’re wanting to place an object on a flat surface and a vert already exists at the desired position - then use that - no need to create a ‘destination’ face.
Exploring the Bounding Box tools (under Tools, top menu) for what you appear to be constructing could also pay dividends, as these let you move stuff around with a great deal of precision - no relative rotations take place (as can happen with PutOn) - but there’s nothing to stop you using both tools, where / if necessary. (more info on the BBox page here - www.puzzledpaul.com)
Again, depending on what you’re doing, Face | Extract Region > Normal > 0 might prove useful (hold shift down during op to constrain to > 0 movement, open Window | Geom. Graph to ‘see / control’ new object(s) ) - as this will provide new reference geometry at exactly the same (destination) position - which you could use as the basis (possibly) for constructing what you want to be there, in the first place.
(rather than making it somewhere else and then moving it)
If the co-ordinates of a destination pont are known (can be found by selecting a single element and eyeballing top left info display) - then You might find the Move | Absolute tools
very useful - especially as you can deposit dupes of the original object 
Other things come to mind, but this’ll do for now - without knowing a few more details 
(I’m assuming you have Advanced Menus enabled, btw - via Edit | Prefs)
pp